Option pricing with conditional GARCH models

Abstract

This paper introduces a class of conditional GARCH models that offers significantly added flexibility to accommodate empirically relevant features of financial asset returns while admitting closed-form recursive solutions for the moment generating function, a variance dependent pricing kernel and, therefore, efficient option pricing in a realistic setting. This class of conditional GARCH models can be constructed with specifications of the GARCH dynamics and innovations, for which recursive moment generating function formulas have been derived, hence generalizing such families of models. As an example, we combine the popular Heston-Nandi model with Regime Switching to illustrate the flexibility of our methodology and demonstrate the importance in terms of option prices and Greeks of accommodating crisis periods and state dependency as well as priced variance risk.